## Abstract

A famous result of Freiman describes the structure of finite sets A {subseteq} Z with small doubling property. If |A + A| ≤ K|A|, then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.

Translated title of the contribution | Freiman's theorem in an arbitrary abelian group |
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Original language | English |

Pages (from-to) | 163 - 175 |

Number of pages | 13 |

Journal | Journal of the London Mathematical Society |

Volume | 75 (1) |

DOIs | |

Publication status | Published - Feb 2007 |